Freeform Optical Surfaces Research Articles

Modelling and simulation of freeform surface generation in ultra-precision raster milling

Optical freeform surfaces are large-scale surface topologies with shapes generally possessing non-rotational symmetry with submicrometric form accuracy and nanometric surface finish. Due to the geometrical complexities, the prediction of form accuracy in ultraprecision raster milling of ultra-precision freeform surfaces is more difficult than conventional machining. Nowadays, the achievement of submicrometre form accuracy still depends largely on the experience and skills of the machine operators through an expensive trial-and-error approach. This paper presents a model-based simulation system for the prediction of form accuracy in ultra-precision raster milling of optical freeform surfaces. The system takes into account the cutting mechanics, cutting strategy, and the kinematics of the cutting process. Experimental work has been undertaken to verify the system and the predicted results agree well with the experimental results. The successful development of the model-based simulation system allows the optimum cutting parameters and cutting strategies to be determined without the need to conduct massive and costly trial-and-error cutting tests.

Theoretical and experimental evaluation of surface quality for optical freeform surfaces

Optical freeform surfaces have become indispensable in the products of photonics and telecommunication. Due to the geometrical complexity and optical particularity, it is difficult to test and evaluate the surface quality of optical freeform surfaces in terms of the form accuracy and surface finish. This paper presents a surface metrology model for the evaluation of surface quality of the optical freeform surfaces. The model is built based on a freeform surface-matching algorithm using the five-points-position-fixed, layered-step, and multilevel method with the match precision higher than 1 nm. Some parameters are also proposed for evaluating the surface quality of the freeform surfaces. The model is validated through a series of simulation and actual measurement experiments. The theoretical results agree well with the experimental results.

Form-Profiling of Optics Using the Geometry Measuring Machine and the M-48 CMM at NIST.

We are developing an instrument, the Geometry Measuring Machine (GEMM), to measure the profile errors of aspheric and free form optical surfaces, with measurement uncertainties near 1 nm. Using GEMM, an optical profile is reconstructed from local curvatures of a surface, which are measured at points on the optic’s surface. We will describe a prototype version of GEMM, its repeatability with time, a measurements registry practice, and the calibration practice needed to make nanometer resolution comparisons with other instruments. Over three months, the repeatability of GEMM is 3 nm rms, and is based on the constancy of the measured profile of an elliptical mirror with a radius of curvature of about 83 m. As a demonstration of GEMM’s capabilities for curvature measurement, profiles of that same mirror were measured with GEMM and the NIST Moore M-48 coordinate measuring machine. Although the methods are far different, two reconstructed profiles differ by 22 nm peak-to-valley, or 6 nm rms. This comparability clearly demonstrates that with appropriate calibration, our prototype of the GEMM can measure complex-shaped optics.

224 リニアモータ搭載型超精密加工機における高精度高加速度制御加工への検討(OS-6 超精密加工)

The demand for free-form optical surfaces has increased in recent years. Presently there are several methods to manufacture such surfaces. The raster fly-cutting, which is one of most common methods, requires long machining cycles and is difficult to set up. Though several newly developed methods such as Fast Tool Servo are proposed some limitations still exist. In this study, it was confimed the possibility of the high accurate and high accelerate controlled machining to achieve the free-form surface with high productivity. In the results, good form accuracy and surface roughness were obtained without any limitations of the stroke and the versatility.

Impact on Diffraction Efficiency of Binary Optical Elements for Spot Exposure Superposing Ratio

In fabrication of free form optical surfaces, spot exposure is a typical mode in laser photolithography. Proper selection of spot exposure superposing ratio is the key to optimize etching quality and writing speed. In this paper, a new composite diffractive grating structure is modeled for the influence on diffraction efficiency of binary optical elements caused by spot exposure superposing ratio. Composite grating can be transformed into one simple rectangular grating and two triangular gratings. Angular spectrum theory is used to describe the mathematical expression of the composite diffractive grating. Through simulation analysis, the relationships between diffraction efficiency and the other three items as grating depth, spot radius, and blaze wavelength, has been shown. Simulation results indicate that shape error caused by spot exposure ratio impact the diffraction efficiency greatly in deep etching, and the transmittance will reach maximal point approximately while spot exposure ratio is over 60%. This conclusion can be taken as the theoretical foundation for exposure frequency selection in laser photolithography figure generation.

Model-based Simulation of Free form Surface Generation in Ultra-precision Raster Milling(Analytical advancement of machining process)

Due to the geometrical complexities, the prediction of form accuracy in ultra-precision raster milling of optical free form surfaces is more difficult than conventional machining. Nowadays, the achievement of submicrometer form accuracy still depends largely on the experience and skills of the machine operators through an expensive trial-and-error approach. In this paper, a model-based simulation system is presented for the prediction of form accuracy in ultra-precision raster milling. The system takes into account the cutting mechanics, cutting strategy and the kinematics of the cutting process. Preliminary experimental work has been done to verify the model and the predicted results agree well with the experimental results. Ultra-precision raster milling is an expensive and complex process, the successful development of the model-based simulation system allows the optimum cutting parameters and cutting strategies to be determined without the need to conduct massive and costly trial-and-error cutting tests.

Tailored freeform optical surfaces.

Freeform optical surfaces embedded in three-dimensional space, without any symmetry, are tailored so as to solve the archetypal problem of illumination design: redistribute the radiation of a given small light source onto a given reference surface, thus achieving a desired irradiance distribution on that surface. The shape of the optical surface is found by solving a set of partial nonlinear differential equations. For most cases, a few topologically distinct solutions exist, given suitable boundary conditions.