Significance  As the performance of optical systems is becoming more and more demanding, complex optical surfaces such as aspheres and free-form surfaces can improve the imaging performance of the system, so it is extremely important to improve the detection accuracy of complex optical surfaces. Interference detection is an important means of measuring complex optical surfaces, and Computer Generated Holograms (CGH), as one of the interferometric detection methods, has been widely used due to its high accuracy and large degree of design freedom. However, the various types of errors existing in the process of CGH detection of complex surfaces will affect the accuracy of wavefront detection. The significance of Computer-Generated Holograms (CGH) in optical surface metrology lies in its transformative potential to achieve unparalleled precision and efficiency in measuring complex surface profiles. Traditional metrology methods often face limitations in accuracy and versatility, particularly when dealing with intricate geometries and microscopic features. In contrast, CGH offers a non-contact, high-resolution approach that promises to revolutionize metrology across various industries, including semiconductor manufacturing, aerospace engineering, and biomedical sciences.

Progress  In the development of Computer Generated Holograms (CGH) technology, the study and management of errors play a crucial role. CGH technology is capable of high-precision surface measurements and morphology reconstruction by utilising the principles of computational optics. However, how to effectively identify, understand and minimise errors is crucial to ensure measurement accuracy. In recent years, researchers have focused on addressing the various sources of error that can exist in CGH systems, which include, but are not limited to, non-uniformities in the optical system, environmental factors (e.g., vibration and temperature variations), and the accuracy of the algorithms themselves. Through systematic error analyses and corrections (Fig.2), researchers have continued to improve the algorithms and hardware designs in order to enhance the stability and measurement accuracy of the CGH system. Specifically, research advances have shown that novel error compensation techniques and advanced data processing algorithms have significantly improved the CGH system's ability to measure complex surfaces. These techniques, including model-based correction methods and real-time feedback control systems, can effectively reduce system errors and improve measurement accuracy and repeatability. Future research directions will further focus on improving the ability of CGH systems to measure surfaces at tiny scales and under non-ideal conditions, such as applications in high or very low temperature environments. In addition, with the advancement of computing power and optical technology, more adaptive error correction methods based on machine learning and artificial intelligence are expected to emerge, which will open up new possibilities for the wide application of CGH technology in industrial production and scientific research.

Conclusions The results presents findings related to each category of CGH errors identified in the study. It discusses the specific mechanisms contributing to design, encoding, and manufacturing errors, supported by relevant literature and experimental data. The section also includes case studies and comparative analyses of calibration methods used to mitigate these errors in practical applications. Discussions expand on the implications of error reduction strategies for improving the accuracy of CGH-based interferometric measurements in various optical testing scenarios. Furthermore, the section examines the limitations of current methodologies and proposes potential avenues for future research aimed at advancing CGH technology in optical surface metrology. In conclusion, the study synthesizes the key findings regarding CGH errors and their impact on measurement accuracy in optical surface metrology. It summarizes the significance of addressing design, encoding, and manufacturing errors to enhance the performance of CGH-based interferometric systems. The conclusions highlight the effectiveness of calibration techniques in minimizing error propagation and improving measurement reliability. Additionally, the section outlines future research directions, emphasizing the need for continued innovation in CGH technology to meet evolving demands in high-precision optical manufacturing and metrology.