J. Eur. Opt. Society-Rapid Publ. 21, 30( 2025) 315
Fig. 5. Camera images; left: original image; right: evaluated image. comparatively small crystal size, the glass ceramic is only partially transparent. Due to their low transparency, LAS glasses are primarily used in mirrors and as a construction material with a low coefficient of thermal expansion. Lithium aluminum silicate glass, with the basic chemical formula Li 2 O – Al 2 O 3 – Si 2 O, has a consistently low Coefficient of Thermal Expansion( CTE) over a wide temperature range. Due to their low coefficient of thermal expansion and high strength, glass ceramics play a crucial role in the production of astro and lithographic mirrors. Zerodur’ s low CTE ensures that the mirror retains its shape and optical accuracy even during temperature fluctuations. This allows for reduced mirror thickness without compromising structural strength. The ability to maintain shape stability due to thermal fluctuations would otherwise require more bulk mirror material. Glass ceramics based on LAS were discovered by Stookey [ 21 ] in 1960 and appears under various brand names, including: Zerodur( Schott, Germany). In this work, Zerodur is used as the material for the samples. Due to the minimal thermal expansion coefficient, the work piece temperature and thus the expansion of the work piece can be neglected. The CTE for Schott Zerodur are between 0 ± 0.1 10 �6 / K and 0 ± 0.007 10 �6 / K in a range of 0 – 50 ° C, with a maximum temperature of 600 ° C.
Polishing fluid and polishing agent carrier are essential factors for the achievable roughness and removal. Polishing with polyurethane foams as a polishing agent carrier and cerium oxide in aqueous suspension as a polishing liquid has established itself as a standard in the industry. As polishing grains Universal Photonics Hastilite PO is used: density of the slurry is 1.5 – 1.68 g / mL with a maximum diameter of 4 lm. About 90 % of the grains are below one micron.
3.2 Software
The purpose of the software module is to calculate and visualize the relative velocity between tool and workpiece based on real-time positional data. It processes motion data collected from the sensor system and computes a velocity distribution map for each polishing cycle. This enables correlation with material removal measurements and forms the computational backbone for future closed-loop control.
Python is a high-level programming language, H. Its further development is coordinated by the non-profit Python Software Foundation. The name“ Jupyter” refers to the three core programming languages: Julia, Python, and R. Numpy is used as a program library, which enables fast processing of the data. In Figure 6 the formula( 8) is shown as programming in Numpy as sketch. Matrices are generated for lateral and rotational velocities, as well as for overlay and final output. The lateral matrix is formed from formula( 10) v xy and the rotational matrix from formula( 10) v rot tool and v rot work piece for the work piece( see Fig. 1, area A1). With full-aperture polishing, the workpiece is smaller than the polishing tool, but occasionally protrudes beyond the tool edge. This is taken into account by the overlay matrix. The third dimension is the representation of the individual images. Adding these together gives the overall result.
For programming the PLC( Programmable Logic Controller) Beckhoff TwinCAT is used. TwinCAT is a software suite providing the environment for creating and running automation applications on PC-based control systems.
4 Validation
The system must be verified to ensure the validity of the results. There are several possibilities to show that the program codes are working properly.
4.1 PLC programming
For the length calibration( to calculate Px into mm) a calibration gauge made of Schott Zerodur glass ceramic, a material with low CTE, was ground with high precision. The distance of two trackers on that gauge is 200 mm ± 2 lm, but the manufacturing accuracy of the trackers is limited due to plastic molding. A black and white image of the gauge with two mounted trackers was saved without evaluation and processed afterwards by an offline Python program. The Python program used standardized algorithms for circle detection from OpenCV( Open computer vision) library. The programming of OpenCV to