Aberrations in optical systems are key factors that influence image quality and optical performance. With the advancement of optical technology, precision optical systems are increasingly being used in various fields, such as remote sensing imaging, medical imaging, and machine vision, where controlling aberrations is particularly essential. In optical systems with reflective devices, such as large astronomical telescopes, the aperture is often designed to be large to achieve enhanced resolution, with the primary mirror typically made up of multiple segmented submirrors. Manufacturing and alignment errors can influence the co-phasing of these submirrors, making reflective system’s aberration measurement and correction crucial in optical engineering. Although aberrations are inherent to optical systems, deviations introduced during the manufacturing and alignment of optical components can also contribute to additional aberrations. Therefore, accurately measuring and analyzing the inherent and additional aberrations of the reflective system can improve the manufacturing process of optical components, optimize system alignment, and enhance the optical system performance. The aberration measurement and analysis process is vital for ensuring high-precision, high-resolution imaging. Traditional measurement methods, such as Foucault knife-edge testing, Ronchi testing, star testing, interferometry, and Shack?Hartmann testing, are used for aberration analysis. Among these, Foucault, Ronchi, and star testing are primarily used for qualitative analysis. Interferometry, a commonly used high-precision measurement method, calculates aberrations in the system from observations of changes in the shape and number of interference fringes. However, interferometric testing has a limited dynamic range, is sensitive to environmental influences, and is expensive, making it impractical for large mirror alignments. Shack?Hartmann testing samples the wavefront using an array of lenses to obtain wavefront slope information. The wavefront can be reconstructed from the integration of slopes, thereby achieving aberration measurements. Although simple and highly precise, Shack?Hartmann testing is limited by the manufacturing precision of the lens array and is a cost-intensive method. Phase measuring deflectometry (PMD), a noncontact and noninterferometric measurement method, has gained popularity for high-precision measurements in various optical systems because of its high accuracy, ease of implementation, and low cost. However, for use in wavefront aberration measurements, PMD requires knowledge of the structural parameters of the optical system to perform ray tracing, which introduces pose errors or errors in complex structures. Therefore, a general method for measuring and aligning wavefront aberrations in optical systems is still lacking.

For efficient wavefront aberration measurement without knowledge of the structural parameters of an optical imaging system, a method based on vision ray calibration deflectometry is proposed in this study. The proposed method captures multiple sets of phase-shifted fringe images from a display at different postures to directly calibrate the directions of the exiting rays from the tested optical system. The wavefront aberrations are then calculated using a wavefront aberration formula, enabling in-situ alignment based on the aberration results. The feasibility of the proposed method was verified through a numerical simulation of an Ritchey?Chrétien (RC) system with a primary mirror aperture (diameter: 150 mm), a radius of curvature of -742.857 mm, and a conic constant of -1.046. The secondary mirror has a radius of curvature of -290.233 mm and a conic constant of -2.915. The wavefront aberration distribution and values obtained from the simulation closely match the theoretical calculations. The experimental results further validate the effectiveness of the proposed method for aberration measurement and alignment in a real RC system and a planoconvex lens. A comparison with interferometry results demonstrate good consistency, confirming the proposed method’s validity.

This study presents a method for in-situ wavefront aberration measurement and alignment of optical systems that does not require system parameters. The proposed method is based on a vision ray calibration model. The method’s effectiveness of the method is validated through numerical simulations and experiments. In the numerical simulation, additional surface features were introduced into the system (Fig. 4), and the results (Fig. 5) demonstrate that the wavefront aberrations obtained using this method are consistent with those derived from theoretical calculations, with nearly identical Zernike coefficients. In the experiment, the method was applied to align and measure an RC system with a primary mirror aperture of 150 mm. The experimental results (Fig. 9) demonstrate that after alignments, the low-order off-axis aberrations are significantly reduced, indicating that the primary and secondary mirrors are nearly coaxial. Additionally, an in-situ measurement and alignment were performed on a planoconvex lens with an effective aperture of approximately 60 mm. The experimental results (Figs. 12 and 13) show that the Zernike coefficients of terms Z5?Z8 are almost zero. After alignments, the wavefront aberration measurement, with the first 10 Zernike terms removed, yields an root mean square (RMS) of 111 nm, which is consistent with the interferometry results. These findings validate the effectiveness of the vision ray calibration?based deflectometry method for wavefront aberration measurement and alignment.

This study proposes a method for in-situ alignment and wavefront aberration measurement for optical imaging systems that does not require structural parameters. The proposed method is based on a vision ray calibration model. The proposed method can be applied for the in-situ measurement and alignment of an RC system, as well as a planoconvex lens. This study first outlines the basic principles of wavefront aberration measurement and the application of vision ray calibration in the measurement process. A numerical simulation of the wavefront aberration measurement optical path of an RC system is presented to analyze the changes in low-order off-axis aberrations due to secondary mirror misalignment. The experimental results of in-situ wavefront aberration measurements and alignments of the RC system and planoconvex lens are presented. The results are consistent with interferometry measurements, thus validating the effectiveness of the proposed method and offering a feasible solution for multimirror system alignment.