J. Eur. Opt. Society-Rapid Publ. 2026, 22, 51 Ó The Author( s), published by EDP Sciences, 2026 https:// doi. org / 10.1051 / jeos / 2026047 Available online at: https:// jeos. edpsciences. org
Journal of the European Optical Society-Rapid Publications
RESEARCH ARTICLE
Modeling and experimental comparison of the plasma jet induced etch front for subsurface damage determination Heike Müller 1,*
, and Thomas Arnold 1, 2 1 Leibniz Institute of Surface Engineering( IOM), Permoserstraße 15, 04318 Leipzig, Germany 2 Institute of Manufacturing, TU Dresden, 01062 Dresden, Germany
Received 25 March 2026 / Accepted 15 May 2026
Abstract. The performance of optical systems can be compromised by subsurface damage( SSD) caused by mechanical processing. This study presents a destructive method of determining SSD depth in fused silica surfaces using atmospheric plasma jet etching( PJE). A simplified mathematical model describes how the etching front evolves under the assumption of isotropic etching. By comparing simulated surfaces with topographies determined experimentally after each etching step, an isotropy factor( IF) is calculated to identify deviations from isotropy. Areas with an IF greater than one exhibit anisotropic etching behavior, indicating the presence of SSD. The method was validated using defined Vickers indentations, scratches and conventionally polished samples. The maximum SSD depth correlates with both the maximum IF value and the slope of the cavity volume versus etching depth. For the samples examined, SSD depths ranged from 6.37 lm to 52.47 lm. The results agreed well with OCT measurements( deviation < 10 %). The developed approach not only enables the quantitative determination of SSD depth, but also the three-dimensional reconstruction of crack morphology. Combining computer-aided modelling with experimental comparison provides a robust method for characterizing the quality of optical components.
Keywords: Atmospheric plasma jet, Plasma jet etching, Subsurface damage, Fused silica.
1 Introduction
The performance of optical systems is continuously improving as a result of a combination of different optical elements, advances in component design and materials, and higher precision of manufacturing techniques. However, numerous factors such as misalignment, coating defects and subsurface damage( SSD) can affect this theoretically high quality. Subsurface damage describes microcracks that occur, for example, as a result of the abrasive surface machining of hard, brittle optical materials( e. g. glass). During the grinding process of optical glass, the abrasive grains cause the material to chip. These random fractures initially result in an optically opaque surface, which later becomes transparent during the subsequent polishing process. However, the grinding process also causes median cracks that extend into the matrix below the chipping and must also be removed by polishing [ 1 ]. It is therefore important to know the maximum depth of the defects.
In optics manufacturing, the SSD depth is estimated by the optical engineer during the manufacturing process
* Corresponding author. heike. mueller @ iom-leipzig. de based on the machining parameters used and the roughness after grinding in order to determine the required material removal during polishing. With sufficient experience, the required polishing removal can be estimated to ensure that the optical element at the end no longer exhibits SSD. Other non-destructive methods are based on light scattering effects caused by damage buried under the defect-free surface. Laser scattering methods such as laser scanning confocal microscopy or total internal reflection microscopy are used as well as optical coherence tomography( OCT) or X-ray diffraction. For the latter, the equipment is very expensive and requires a vacuum pumping system which impedes sample handling, so this technique is rarely used for SSD determination [ 2 – 4 ].
In addition to the development of non-destructive testing methods, destructive testing is still state of the art. Most of these techniques are based on the preparation of a crosssectional view, such as bevel or dimple polishing but also focused ion beam( FIB) to determine the depth-extent of the damage by microscopic observation( e. g. optical microscopy or transmission electron microscopy). Those preparation techniques can only give information about a specific cross-sectional view. A more global distribution of the SSD can be detected after applying wet chemical etching
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