Modelling of coherence scanning interferometry for complex surfaces based on a boundary element method

Thomas, Matthew; Su, Rong; Nikolaev, Nikolay; Coupland, Jeremy; Leach, Richard

Abstract

Coherence scanning interferometry (CSI) is a well-established technique for measuring surface topography based on the coherence envelope and phase of interference fringes. The most commonly used surface reconstruction methods, i.e. frequency domain analysis, the envelope detection method, and the correlogram correlation method, obtain the phase of the measured field for each pixel and, from this obtain the surface height, by assuming the two are directly proportional. For surfaces with minor deviations from a plane, it is straightforward to show that the scattered field's phase is a linear function of surface height. An alternative approach known as the "foil model" gives more generally the scattered field as the result of a linear filtering process operating on a "foil" representation of the surface. This model assumes that the surface slowly varies on the optical scale and that there is no multiple scattering. However, for surfaces that are rough at the optical scale or have coherent features (e.g. vee-grooves), the effect of multiple scattering cannot be neglected and remains a problem for reconstruction methods. Linear reconstruction methods cannot provide accurate surface topographies for complex surfaces, since for such surfaces, the measurement process of CSI is fundamentally non-linear. To develop an advanced reconstruction method for CSI, an accurate model of the imaging process is required. In this paper, a boundary elements method is used as a rigorous scattering model to calculate the scattered field at a distant boundary. Then, the CSI signal is calculated by considering the image formation as back-propagation of the scattered field, combined with the reflected reference field. Through this approach, the optical response of a CSI system can be predicted rigorously for almost any arbitrary surface geometry. Future work will include a comprehensive experimental verification of this model, and development of the non-linear surface reconstruction algorithm.

Citation

Thomas, M., Su, R., Nikolaev, N., Coupland, J., & Leach, R. (2019). Modelling of coherence scanning interferometry for complex surfaces based on a boundary element method. Proceedings of SPIE, 11057, 1-12. https://doi.org/10.1117/12.2526015

• Journal Article Type: Conference Paper
• Conference Name: Modeling Aspects in Optical Metrology VII
• Conference Location: Munich, Germany
• Start Date: Jun 24, 2019
• End Date: Jun 26, 2019
• Acceptance Date: Apr 25, 2019
• Online Publication Date: Jun 26, 2019
• Publication Date: Jun 21, 2019
• Deposit Date: Jun 18, 2019
• Publicly Available Date: Jul 3, 2019
• Journal: Proceedings of SPIE
• Print ISSN: 0277-786X
• Electronic ISSN: 1996-756X
• Publisher: Society of Photo-optical Instrumentation Engineers
• Peer Reviewed: Peer Reviewed
• Volume: 11057
• Article Number: 1105713
• Pages: 1-12
• DOI: https://doi.org/10.1117/12.2526015
• Keywords: coherence scanning interferometry; optical modelling; microscopy; computational electromagnetics
• Public URL: https://nottingham-repository.worktribe.com/output/2203410
• Publisher URL: https://www.spiedigitallibrary.org/conference-proceedings-of-spie/11057/2526015/Modelling-of-coherence-scanning-interferometry-for-complex-surfaces-based-on/10.1117/12.2526015.short
• Related Public URLs: https://spie.org/EOM/conferencedetails/modeling-aspects-optical-metrology#session-8
• Additional Information: Copyright 2019 Society of Photo-Optical Instrumentation Engineers. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited.