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• We analyze the problem areas and distorted signals that can arise when measuring CSMU using basic white-light interferometry. We specifically focus on addressing the structural areas that are prone to errors, ensuring reliable processing results and improving efficiency. • In the signal processing of the problem areas, we employ characteristic analysis of the distorted signal. By filtering out the disturbed part of the signal and extracting the desired portion containing accurate height information, we are able to reconstruct the 3D topography. • This algorithm can be applied to any traditional optical system utilizing white-light interferometry. It is a simple and accurate approach that only requires a standard experimental setup, making it highly practical. Micro-nanostructures refer to technologies that operate at the nanoscale and provide materials and devices with unique mechanical, physical, and chemical properties. These structures have diverse applications in fields such as microelectronics, biotechnology, aerospace, and metamaterials. As precision machining technology advances, the demand for smaller sizes and higher accuracy of structural units has increased, leading to more compact integration. Consequently, the lossless and high-precision 3D measurement of highly integrated micro-nanostructure components has become increasingly challenging. In this study, we analyzed measurement errors in compactly spaced microstructural units using white-light scanning interferometry and proposed an algorithm to optimize this technology. By combining coherent peak-histogram processing with signal correlation analysis, we were able to improve the measurement accuracy by approximately ten times compared to current mainstream algorithms. To validate our algorithm, we performed experiments using metasurfaces with structural unit spacing at the order of sub-micrometer. The results obtained demonstrated the effectiveness of our algorithm in achieving accurate measurements. [ABSTRACT FROM AUTHOR]

It is imperative to achieve the co-phase state for large segmented mirrors of telescopes. This paper proposes a novel method for quantifying the co-phase errors of the segmented mirrors, as well as to detect any residual errors by analyzing the surface shape of segmented mirrors using conformal mapping after the correction of the co-phase errors, aiming to achieve a more precise co-phase state. This method applies a dual-wavelength phase-shifting interferometry based on optical vortex to measure the co-phase errors (i.e., tip, tilt, and piston), and measures the surface shape of segmented mirrors based on conformal mapping phase-shifting interferometry to identify which kind of co-phase errors still exist there, and then adjust the segmented mirrors to achieve a more precise co-phase state. The functional relationships between piston error or tip/tilt error and phase distribution in the image plane are derived, and the mathematical tool of conformal mapping is used for surface shape demodulation. The experiment results indicate that the resolution of the piston error measurements is 1.878 nm, and the resolution of the tip/tilt error measurements is 0.760″. Furthermore, the surface shape measurement after adjustment based on conformal mapping phase-shifting interferometry is 7.503 nm (RMS). [ABSTRACT FROM AUTHOR]

• A simple and effective strategy is proposed to measure the focal lengths. • It enables non-contact measurement and no need to measure the distance between optics components. • The entire measurement system occupies a small space that is easy to set up and operates. This paper proposes a new method to measure the focal lengths of both convex and concave lenses based on vortex beam interference. Theoretical analysis illustrates that the maximum intensity distribution of the interferogram is in accordance with the Fermat's spiral, and the spiral coefficient is proportional to the difference between the focal length of the test lens and the distance from the test lens to the camera. In order to calculate the precise focal length, we separately block the light paths to obtain the reference and test beam spots, and get the ratio of these two spot sizes. Then, the ratio and the spiral coefficient are used to determine the focal length. For a biconvex lens with a focal length of 200 mm and a biconcave lens with a focal length of −100 mm, the relative measurement errors are 0.0892 % and 0.0800 %, respectively. This research provides a novel and convenient method for measuring the focal length, and no-sophisticated displacement devices and moving the lens to be measured are required in the measurement. [ABSTRACT FROM AUTHOR]