Computer-Based Simulation of Deformation of a Quartz Biconvex Lens During Vacuum Mounting in an Interferometer

Modern projection optical systems, such as DUV lithography and high-numerical-aperture objectives, require extremely high surface machining accuracy, making the consideration of mechanical deformations of optical elements particularly critical. This paper presents the results of a computer simulation of the deformation of a 195 mm diameter fused silica biconvex lens under vacuum. The study was performed in CAE (Computer-aided engineering) software suites employing different calculation algorithms. A lens model designed in a CAD (Computer-aided design) system was used. The lens material is fused silica with a Young’s modulus of 72 GPa and a Poisson’s ratio of 0.17. It was established that an operational pressure differential of 15 kPa causes non-uniform deformation of the lens surface, with maximum values ranging from 22.59 to 23.24 nm, depending on the calculation algorithm. The discrepancy between the results was 2.8 %. A linear dependence of deformation on the pressure differential was established: as the pressure differential changes from 0 to 18 kPa, the deformation increases from 0.75 to 27.74 nm. The greatest surface distortion is observed in the central zone of the lens, which is critical for interferometric measurements requiring nanometer-level accuracy. The results underscore the necessity of adjusting vacuum mounting parameters to minimize deformations and improve the quality of optical surface machining.

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