Comparison of form measurement results for optical aspheres and freeform surfaces

Comparing form measurement data for aspheres and freeform surfaces is an important tool for ensuring the quality and functionality of the devices used to take such measurements and may also allow the underlying measurement methods to be evaluated. However, comparing the highly accurate form measurements of such complex surfaces is a demanding task. It is difficult to analyze measurement results whose accuracies are in the range of several tens of nanometers root-mean-square, especially when comparing data with different, and anisotropic distributions of the 3D measurement points on the surface under test. In this paper, we investigate eight different 3D measurement point distributions that are typical of highly accurate measurement systems currently in use and demonstrate the effects of these distributions on the comparison results by using virtually generated data and applying different evaluation strategies. The results show that, for the examples investigated, the different 3D measurement point distributions can yield different levels of accuracy for the comparison. Furthermore, an improved evaluation procedure is proposed and recommendations on how to significantly reduce the influence of the different 3D measurement point distributions on the comparison result are given. A method of employing virtually generated test data is presented that may be generalized in order to further improve and validate future comparison methods.

Development of a metrological reference system for the form measurement of aspheres and freeform surfaces based on a tilted-wave interferometer

Aspheres and freeform surfaces play an important role in today's optics industry. However, the measurement of such complex surfaces is still challenging even with state-of-the-art manufacturing technology, and there is an urgent need in industry for a non-contact, highly accurate reference measurement technique. To meet this demand, at PTB, a metrological reference system for the contact-free form measurement of aspheres and freeform surfaces is under development. The measurement system is based on a tilted-wave interferometer. Advances in computational capabilities have made it possible to solve the complex inverse problems associated with this measurement system and to develop sophisticated analysis procedures for reconstructing the surface under test from the measured interferogram data. In this paper, we will present the status of the tilted-wave interferometer-based measurement system at PTB, describe the analysis procedures we have designed and show initial measurement results. The benefit of the implementation presented here is that it allows insight to be gained into the performance of the measurement system and enables traceable measurements to be established with low uncertainty.

A Review of designing freeform optical surfaces by the Monge–Ampère equations

Background: The equations of Monge–Ampère type which arise in geometric optics is used to design illumination lenses and mirrors. The optical design problem can be formulated as an inverse problem: determine an optical system consisting of reflector and/or refractor that converts a given light distribution of the source into a desired target light distribution. For two decades, the development of fast and reliable numerical design algorithms for the calculation of freeform surfaces for irradiance control in the geometrical optics limit is of great interest in current research. Objective: The objective of this paper is to summarize the types, algorithms and applications of Monge–Ampère equations. It helps scholars to grasp the research status of Monge–Ampère equations better and to explore the theory of Monge–Ampère equations further. Methods: This paper reviews the theory and applications of Monge–Ampère equations from four aspects. We first discuss the concept and development of Monge–Ampère equations. Then we derive two different cases of Monge–Ampère equations. We also list the numerical methods of Monge–Ampère equation in actual scenes. Finally, the paper gives a brief summary and an expectation. Results: The paper gives a brief introduction to the relevant papers and patents of the numerical solution of Monge–Ampère equations. There are quite a lot of literatures on the theoretical proofs and numerical calculations of Monge–Ampère equations. Conclusion: Monge–Ampère equation has been widely applied in geometric optics field since the predetermined energy distribution and the boundary condition creation can be well satisfied. Although the freeform surfaces designing by the Monge–Ampère equations is developing rapidly, there are still plenty of rooms for development in the design of the algorithms.

Characterization of specular freeform surfaces from reflected ray directions using experimental ray tracing

The applications of freeform surfaces in optical components and systems are increasing more and more. Therefore, appropriate measurement techniques are needed to measure these freeform surfaces for verification. This task is still a challenge for most measurement techniques. In this paper, we propose a measurement technique for optical and other specular freeform surfaces based on experimental ray tracing. This technique is able to measure form and mid-spatial-frequency deviations simultaneously. The focus will be set on the sensing technique and the measurement uncertainties in the setup. As the measurement technique is described, an estimation of the influence of different uncertainties based on simulations is given. The result from an experimental measurement is evaluated in relation to the influence of the uncertainties. A comparison measurement for evaluation is given.