31 August 2005 Monte Carlo analysis for the determination of the conic constant of an aspheric micro lens based on a scanning white light interferometric measurement
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Abstract
Characterizing an aspheric micro lens is critical for understanding the performance and providing feedback to the manufacturing. We describe a method to find the best-fit conic of an aspheric micro lens using a least squares minimization and Monte Carlo analysis. Our analysis is based on scanning white light interferometry measurements, and we compare the standard rapid technique where a single measurement is taken of the apex of the lens to the more time-consuming stitching technique where more surface area is measured. Both are corrected for tip/tilt based on a planar fit to the substrate. Four major parameters and their uncertainties are estimated from the measurement and a chi-square minimization is carried out to determine the best-fit conic constant. The four parameters are the base radius of curvature, the aperture of the lens, the lens center, and the sag of the lens. A probability distribution is chosen for each of the four parameters based on the measurement uncertainties and a Monte Carlo process is used to iterate the minimization process. Eleven measurements were taken and data is also chosen randomly from the group during the Monte Carlo simulation to capture the measurement repeatability. A distribution of best-fit conic constants results, where the mean is a good estimate of the best-fit conic and the distribution width represents the combined measurement uncertainty. We also compare the Monte Carlo process for the stitched data and the not stitched data. Our analysis allows us to analyze the residual surface error in terms of Zernike polynomials and determine uncertainty estimates for each coefficient.
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Solomon A. Gugsa, Solomon A. Gugsa, Angela Davies, Angela Davies, } "Monte Carlo analysis for the determination of the conic constant of an aspheric micro lens based on a scanning white light interferometric measurement", Proc. SPIE 5878, Advanced Characterization Techniques for Optics, Semiconductors, and Nanotechnologies II, 58780B (31 August 2005); doi: 10.1117/12.617528; https://doi.org/10.1117/12.617528
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