Jiasheng Lu

This paper introduces an adaptive pinhole point diffraction interferometer (PPDI) integrated with a liquid crystal on silicon spatial light modulator (LCOS-SLM) to address the limitations of conventional adaptive optics (AO) systems in measuring large-asphericity surfaces. Conventional adaptive optics (AO) which is usually combined with a common path interferometer, is confined to measuring surfaces comparable to the beam spot size (usually 10 mm to 20 mm), and its commonly employed deformable mirror (DM) exhibits limited lateral resolution. By utilizing the LCOS-SLM's high-definition phase modulation capability, the system dynamically modifies diffracted wavefronts to compensate for high-order aspheric aberrations while expanding the lateral measurement range through non-common-path PPDI optics. The proposed method synthesizes aspheric wavefronts via Zernike polynomial-based patterns (specifically utilizing the defocus term, Z ₄ loaded onto the LCOS-SLM), enabling precise surface profile retrieval through phase-shifting interferometry. Experimental validation on both a parabolic and a 6 ^th -order aspheric mirror demonstrated measurement accuracy with root-mean-square (RMS) deviations below λ/25, confirming the efficacy of LCOS-SLM-driven wavefront compensation. The integration of PPDI and LCOS-SLM eliminates aperture constraints imposed by traditional AO compensators. In principle, as long as the numerical aperture (NA) of the measured surface is smaller than that of the PPDI-generated testing wavefront, the approach is geometrically scalable to larger apertures. Furthermore, LCOS-SLM overcomes the low wavefront modulation resolution inherent in deformable mirrors (DM), and enables high-order aberration-based wavefront modulation through a developed LCOS-SLM pattern generation program. This approach provides a scalable solution for rotationally symmetric aspheric surface metrology in applications such as extreme ultraviolet lithography and precision optical manufacturing.

To address the challenges of insufficient accuracy and poor versatility faced by conventional interferometers in measuring high-order aspheric surfaces, this paper proposes an optimized annular sub-aperture stitching method based on a reverse global planning strategy. The method initiates sub-aperture division from the edge region with the highest asphericity, aiming to maximize the effective measurement range of each individual sub-aperture and setting the minimization of the number of sub-apertures (N) as the core optimization objective. The algorithm features a concise structure, high stability, and ease of automation, enabling a significant extension of the interferometer's dynamic measurement range. Simulation studies demonstrate that the method effectively reduces the required number of sub-apertures, thereby suppressing the propagation and accumulation of mechanical positioning errors during the stitching process. Furthermore, by integrating this method with pinhole point diffraction interferometry (PPDI), a measurement system combining high accuracy and large measurement range is constructed. Experimental measurements of a convex high-order aspheric surface yield stitched results that are in excellent agreement with full-aperture measurements, with the peak-to-valley (PV) deviation of only 2.66 nm and the root-mean-square (RMS) deviation of only 0.44 nm. A detailed uncertainty analysis of the system confirms the reliability and reproducibility of the measurement results. This study not only provides an efficient method for the precision measurement of aspheric surfaces with large deviations but also offers a new technical pathway for enhancing the measurement capability and automation level of interferometers.

Precision measurement of aspherical mirrors is critical for high-end optical systems, where surface accuracy directly impacts performance. However, there remain challenges in this task: 1) measurement precision in large scope; 2) larger ranges and flexibility in complex surface test; 3) environmental robustness in applications; 4) efficiency and accuracy in data processing. This study introduces a novel Multi-Wavelength Point Diffraction Interferometry (MPDI) method, significantly enhancing measurement flexibility and accuracy. Through the diffraction, high-accuracy wavefront (λ/10^-4) is produced to perform relative measurement to aspherical mirrors. By integrating a triple-wavelength laser module and utilizing the beat frequency concept, the system generates at least nine equivalent wavelengths (245.8 nm to 3334.2 nm), enabling efficient testing of mirrors with both large surface deviations and high-resolution requirements. A key innovation is the random two-step phase retrieval method, which improves measurement efficiency by nearly 60% compared to conventional four-step methods, while minimizing the effects of environmental disturbances. The proposed system, equipped with machine vision alignment, ensures precise optical path alignment and enhances wavefront quality. Experimental results show a 5.3-fold increase in measurement range and RMS errors as low as 0.6∙10^-3λ (λ = 633 nm), with stitching-free testing. This MPDI method offers substantial improvements in measurement range, robustness, and efficiency, making it a valuable tool for precision aspherical mirror metrology.

In the pinhole point diffraction interferometer (PPDI), proper alignment between the reflection spot of the tested component and the pinhole is critical to obtain accurate interferograms. At present, adjusting for tilt error requires manual manipulation, and defocus error cannot be corrected. These limitations impede the instrumentation process of PPDI. To address this issue, the proposed tested mirror alignment system utilizes diffraction theory to analyze the mathematical error caused by the misalignment of the tested mirror’s reflected beam and pinhole. An alignment system based on machine vision was designed according to specific requirements. This system incorporates a CCD camera with a zoom lens, the classic PPDI with a pinhole substrate containing a lithography-made mark, and a 3-DOF stepper motor adjusting frame to mount the tested mirror. Additionally, image processing algorithms and step motor driving programs were applied to achieve precise alignment. The system implementation and experimental results indicated that the tilt errors are well-controlled, achieving the defocus error modification, making the interferogram acquisition process more convenient. From the results, this system offers desirable precision and efficiency for PPDI’s tested mirror alignment.

Phase unwrapping method based on Residual Auto Encoder Network is proposed in this chapter. Phase unwrapping is regarded as a multiple classification problem, and it will be solved by the trained network model. Through training and validation stages, optimal network models can be served as predictors of wrap count distribution map of wrapped phase. Then merge the wrapped phase and count together to complete unwrapping. Software simulation and hardware acquisition are the sources of training dataset. To further improve accuracy of unwrapping, image analysis-based optimization method is designed that can remove misclassification and noise points in initial result. In addition, phase data stitching by Iterative Closest Point is adopted to realize dynamic resolution and enhance the flexibility of method. Point diffraction interferometer and multi-step phase extraction technique is the foundation of proposed method. It can be concluded from experiments that the proposed method is superior to state-of-art ones in accuracy, time efficiency, anti-noise ability, and flexibility. Request access from your librarian to read this chapter's full text.

In point diffraction interferometer (PDI), alignment error between objective convergent spot and diffraction pinhole is inevitable during the tests. This phenomenon will affect the performance of PDI in follow aspects: 1) great wavefront error; 2) reduction on diffraction efficiency; 3) quality of interferograms. All these factors may finally reduce the measurement precision of the instrument. Aimed at these technical challenges, we propose machine vision assisted precision alignment system for PDI optical path calibration. Firstly, Rayleigh-Sommerfeld vector diffraction theory is used to build mathematical model among alignment error, diffraction wavefront error, numerical aperture, and pinhole size. To satisfy the requirement of error calibration, scheme of machine vision assisted optical path alignment system is designed. Then we adopt magnetron sputtering and electron beam lithography to fabric precision diffraction pinhole. In this stage, alignment images as well as PDI diffraction efficiency (intensities ratio between reflected and diffracted beam) are the dominant information to determine alignment error in multi-directions. In addition, specialized image processing algorithm is designed that can measure alignment error in pixel and physical scope. To realize automatic correction, mathematical model between measurement and control quantities is constructed. Finally, implementation and experiment of this method are also introduced. Misalignment on lateral translation (XOY plane), longitudinal defocus (optical axis Z) and tilt error (XY tile) are well calibrated and the quality of interferograms is also improved. It can be concluded that the proposed system has advantages in accuracy and efficiency of optical path alignment.

We report a phase-shifting method based on a pinhole point diffraction interferometer. Using the random two-frame phase-shifting algorithm, the piezo electric transducer (PZT) drives the pinhole moving a certain step length along the axis of the tested aspheric mirror. In each step, the CCD collects an interferogram. Then two interferograms are processed by the phase-shifting algorithm. After that, we can acquire the phase map of the interferograms. This technique has great potential for increasing the measuring aperture of the aspheric mirror in the pinhole point diffraction interferometer (PPDI) under the premise of keeping the advantages of PPDI of which the optic devices, as well as error sources, are few behind the substrate.