Search citation statements
Paper Sections
Citation Types
Year Published
Publication Types
Relationship
Authors
Journals
To accurately measure the surface figure of curved mirrors with large radius of curvature (RoC) using stitching interferometry methods, three types of measurement errors are systematically studied, including retrace error, defocusing error within a single subaperture, and stitching angle error among different subapertures. It was found that part of the retrace error caused by the mismatch between the reference wavefront and reflected wavefront has little effect, while the overall retrace error, including the influence of the imperfect optical elements, will cause an error of 1–2 nm RMS within a single subaperture. Defocusing error will enlarge the error due to amplification of optical path error caused by the deviation of the position of the CCD. Because the error is mainly in the edge area, a slope threshold, which controls the maximum surface slope of each subaperture, can be optimized to reduce the effect of the defocus on stitching measurement error. Constant angle error among neighboring subapertures has the biggest accumulation effect on the final stitched figure. For the spherical mirror with RoC of 100 m of 80 m m × 40 m m , the error of the one-dimensional residual profile is 4.67 nm PV, assuming a constant angle error of 2 × 10 − 7 r a d . For the elliptical mirror with RoC of 60–140 m, it is more than 15 nm peak-to-valley (PV). It is because the profile difference caused by constant angle error is closer to a circle, which can be mostly removed after subtraction of a best-fit sphere. Based on the above error analysis, the developed algorithm-based stitching method was used to measure an elliptical cylindrical mirror of 74 m m × 40 m m with RoC of 60–140 m, and the result was compared with a slope measurement instrument from the Beijing Synchrotron Radiation Facility. After removing the best fitting ellipse profile, the one-dimensional difference between the two results is only 0.77 nm RMS, which demonstrated good measurement accuracy.
To accurately measure the surface figure of curved mirrors with large radius of curvature (RoC) using stitching interferometry methods, three types of measurement errors are systematically studied, including retrace error, defocusing error within a single subaperture, and stitching angle error among different subapertures. It was found that part of the retrace error caused by the mismatch between the reference wavefront and reflected wavefront has little effect, while the overall retrace error, including the influence of the imperfect optical elements, will cause an error of 1–2 nm RMS within a single subaperture. Defocusing error will enlarge the error due to amplification of optical path error caused by the deviation of the position of the CCD. Because the error is mainly in the edge area, a slope threshold, which controls the maximum surface slope of each subaperture, can be optimized to reduce the effect of the defocus on stitching measurement error. Constant angle error among neighboring subapertures has the biggest accumulation effect on the final stitched figure. For the spherical mirror with RoC of 100 m of 80 m m × 40 m m , the error of the one-dimensional residual profile is 4.67 nm PV, assuming a constant angle error of 2 × 10 − 7 r a d . For the elliptical mirror with RoC of 60–140 m, it is more than 15 nm peak-to-valley (PV). It is because the profile difference caused by constant angle error is closer to a circle, which can be mostly removed after subtraction of a best-fit sphere. Based on the above error analysis, the developed algorithm-based stitching method was used to measure an elliptical cylindrical mirror of 74 m m × 40 m m with RoC of 60–140 m, and the result was compared with a slope measurement instrument from the Beijing Synchrotron Radiation Facility. After removing the best fitting ellipse profile, the one-dimensional difference between the two results is only 0.77 nm RMS, which demonstrated good measurement accuracy.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.