In critical fields such as precision measurement systems, high-power lasers, and large astronomical telescopes, lenses serve as core components and have extremely high requirements for surface quality. Surface topography detection is a key step in the quality control of precision optical lenses. Digital holography, as a measurement method featuring full-field detection, non-interference, and high sensitivity, can measure multiple parameters of samples such as lenses including surface profiles and refractive indices. In digital holography, the quality of image reconstruction during numerical reconstruction determines the accuracy of the acquired 3-D profile. Approaches to improving the quality of reconstructed images typically involve two aspects: eliminating direct transmitted light and conjugate images, and discriminating the optimal reconstruction distance. In terms of determining the optimal reconstruction distance, multiple focus evaluation algorithms have been developed to achieve autofocusing. However, commonly used conventional focus evaluation algorithms lack universality. Although new discriminant function algorithms proposed in recent years can determine the optimal reconstruction distance, they still have certain limitations. For example, during the search process, they still require manual determination of an approximate range for traversal discrimination, failing to achieve full autonomy. Additionally, their applicability remains limited. To enhance the quality of reconstructed images, this study focuses on determining the optimal reconstruction distance by adopting optimized focus evaluation functions and search algorithms to achieve precise autofocusing, thereby enabling accurate measurement of the 3-D surface profile of the lens.

This study addressed the problem of autofocusing imaging through two aspects: spectrum filtering and optimal reconstruction distance discrimination. Regarding spectrum filtering, a mask-based spectrum filtering technique was adopted to accurately extract the +1 order spectrum, and its effectiveness was verified through comparative experiments using imaging maps and 3-D profile maps. For optimal reconstruction distance discrimination, considering the unique structural characteristics and reconstructed imaging features of plano-convex (plano-concave) lenses, a new segmented discrimination method was proposed. Theoretical analyses were conducted on the improved focus evaluation function and segmented search algorithm, and comparative experiments were conducted with multiple focus evaluation functions to validate the effectiveness of the proposed discrimination method. An off-axis digital holographic optical system was constructed to acquire 3-D profiles of lenses with multiple curvature radii. The calculated radius values were then compared with nominal values to verify reliability.

Comparative experimental results from imaging maps (Fig.3) and 3-D profile maps (Fig.4) demonstrated that compared with basic square filtering, mask-based spectrum filtering with an appropriate threshold could accurately extract the +1 order spectrum. Comparative experiments with multiple focus evaluation functions (including spatial-domain-based, frequency-domain-based, and cosine-score-based functions between axially adjacent images) showed (Fig.6) that only the improved frequency-domain focus evaluation curve exhibited distinct maximum points at 267 mm and 323 mm, enabling precise localization of the optimal reconstruction distances across different regions. Meanwhile, from the results of coarse and fine traversal evaluation curves (Fig.11 and Fig.12), it could be concluded that the segmented search algorithm could achieve full-process autofocusing without manually determining the optimal reconstruction distance range. Utilizing the constructed off-axis digital holographic optical system, high-definition 3-D profile maps of multiple plano-convex lenses were acquired, visually presenting their surface topography characteristics (Fig.13). The relative error between the curvature radii calculated by data fitting and the standard values was controlled within 1% (Table 1), indicating that the proposed technique effectively improved the measurement accuracy.

To achieve accurate measurement of 3-D profiles of the lenses, this study proposes a measurement method integrating digital holography with autofocusing discrimination technology. By analyzing the structural characteristics of lenses and the characteristics of reconstructed imaging, an improved focus evaluation function and a segmented search algorithm are adopted to achieve precise autofocusing and determine the optimal reconstruction distance. Experiments on lenses with multiple curvature radii show that the relative error between fitted results and nominal values is controlled within 1%, verifying the feasibility and effectiveness of the measurement method for detecting the surface profiles of the lenses. Furthermore, this study provides a reference for the application of digital holography in automated 3-D profile detection of lenses.