Mathematical model for optical smoothing prediction of high-spatial-frequency surface errors:
Abstract
This paper describes a mathematical model, called the Bridging model, for predicting the smoothing of high spatial frequency surface errors in optical surfaces during polishing processes, which use large flexible polishing laps. The mathematical model is developed in two stages. First, the Kirchoff flat plate equation, which is modified to include the effect of shear flexibility of the lap and compressive stiffness of the pitch, is solved for lap pressure distribution over a surface error feature represented by a sinusoidal spectrum. This pressure distribution is used as an input to the Preston's equation for material removal rate. The resulting equation is then solved for material removal and surface error smoothing predictions. Available data from a laboratory test and a real optics fabrication program are compared with analytical predictions of the mathematical model. Good correlation is obtained between the two.
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Various tool types have been developed including multilayer elastic tools, viscoelastic tools (like Newtonian fluids), semi-flexible tools (e.g. thin metal layer), viscoplastic (pitch) tools, and mechanically driven tools.
“Various tool types have been developed including multilayer elastic tools, viscoelastic tools (like Newtonian fluids) [18, 30, 31], semi-flexible tools (e.g. thin metal layer) [17, 19, 20], viscoplastic (pitch) tools [19, 27, 28, 32], and mechanically driven tools[33].”
From Smoothing tool design and performance during subaperture glass polishing (2023) · cites this paper as [27]
Existing models on the removal of MSF ripples are based on concepts similar to the workpiece-tool mismatch mechanism described above.
“Existing models on the removal of MSF ripples are based on concepts similar to the workpiece-tool mismatch mechanism described above [26-29].”
From Smoothing tool design and performance during subaperture glass polishing (2023) · cites this paper as [27]
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Smoothing tool design and performance during subaperture glass polishing
Suratwala, T., Tham, G., Steele, R., Wong, L., Menapace, J., Ray, N., & Bauman, B. (2023) · Applied Optics · doi:10.1364/ao.482739 · Cited by 11 · see citing works
- Authors
- Mehta, P. K., & Reid, P. B.
- Affiliations
- Raytheon (United States) (US)
- Venue
- SPIE Proceedings
- Publisher
- SPIE
- Published
- 1999-09-28
- Volume
- 3786
- Pages
- 447-459
- ISSN
- 0277-786X (ISSN-L)
- OpenAlex
- W2066273619
- Cited by
- 23
- References
- 0
- Citations by year
- 2026: 1 · 2025: 2 · 2023: 1 · 2021: 1 · 2020: 1 · 2017: 1 · 2015: 1 · 2014: 5 · 2013: 4 · 2012: 1
- FWCI
- 2.57
- Type
- conference paper
- Language
- en
- Open access
- closed
- Locations
- Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE (publishedVersion)
- Topics
- Physical Sciences › Engineering › Biomedical Engineering › Advanced Surface Polishing Techniques
- Physical Sciences › Engineering › Computational Mechanics › Surface Roughness and Optical Measurements
- Physical Sciences › Engineering › Biomedical Engineering › Advanced optical system design
- Keywords
- bridging model, Preston equation, material removal rate, compressive stiffness, shear flexibility, optical polishing
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